SGMs. 
Inspired by non-equilibrium statistical physics,
[1]} first proposed to destroy the data distribution through a diffusion process slowly,
and learn the backward process to restore the data.
Later on, [2]} explored score matching for generative models by introducing the noise conditional score network (NCSN).
[3]} further scaled
NCSN for higher resolution image generation (e.g., \(256\times 256\) )
by scaling noises and improving stability with moving average.
Interestingly, [4]} summarized all the previous SGMs into a unified framework based on the stochastic differential equation, and proposed the NCSN++ model to generate high-resolution images via numerical SDE solvers for the first time.
[5]} introduced a more complex critically-damped Langevin diffusion (CLD) based SGMs based on Hamiltonian Monte Carlo methods [6]}, where the diffuison process is also guided by a coupled velocity dynamic.
On the contrary, [7]} proposed to restrict the diffusion process on a series of smaller linear subspaces to reduce the computational cost.
As a variant of SGMs, [8]} introduced the denoising diffusion probabilistic models (DDPMs) trained by decreasing the variational bound on generative log-likelihood.
[9]} improved the training of DDMPs through learning the noise variance and reducing the gradient noise.
[10]} developed a cascaded DDPM to generate images at increased resolutions.
Commonly, the existing SGMs use isotropic Gaussian distributions for the diffusion sampling. In this work, we prove that this prevents the SGMs from leveraging the structural distributional priors of target data and leads to slow convergence. We further propose a novel TDAS method to solve this fundamental limitation.
